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openssl/crypto/ec/asm/ecp_nistz256-armv4.pl
Andy Polyakov dfde4219fd ec/asm/ecp_nistz256-*.pl: addition to perform stricter reduction. 
Addition was not preserving inputs' property of being fully reduced.

Thanks to Brian Smith for reporting this.

Reviewed-by: Rich Salz <rsalz@openssl.org>
2016-08-24 10:44:56 +01:00

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#! /usr/bin/env perl
# Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved.
#
# Licensed under the OpenSSL license (the "License"). You may not use
# this file except in compliance with the License. You can obtain a copy
# in the file LICENSE in the source distribution or at
# https://www.openssl.org/source/license.html
# ====================================================================
# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
# project. The module is, however, dual licensed under OpenSSL and
# CRYPTOGAMS licenses depending on where you obtain it. For further
# details see http://www.openssl.org/~appro/cryptogams/.
# ====================================================================
#
# ECP_NISTZ256 module for ARMv4.
#
# October 2014.
#
# Original ECP_NISTZ256 submission targeting x86_64 is detailed in
# http://eprint.iacr.org/2013/816. In the process of adaptation
# original .c module was made 32-bit savvy in order to make this
# implementation possible.
#
# with/without -DECP_NISTZ256_ASM
# Cortex-A8 +53-170%
# Cortex-A9 +76-205%
# Cortex-A15 +100-316%
# Snapdragon S4 +66-187%
#
# Ranges denote minimum and maximum improvement coefficients depending
# on benchmark. Lower coefficients are for ECDSA sign, server-side
# operation. Keep in mind that +200% means 3x improvement.
$flavour = shift;
if ($flavour=~/\w[\w\-]*\.\w+$/) { $output=$flavour; undef $flavour; }
else { while (($output=shift) && ($output!~/\w[\w\-]*\.\w+$/)) {} }
if ($flavour && $flavour ne "void") {
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
die "can't locate arm-xlate.pl";
open STDOUT,"| \"$^X\" $xlate $flavour $output";
} else {
open STDOUT,">$output";
}
$code.=<<___;
#include "arm_arch.h"
.text
#if defined(__thumb2__)
.syntax unified
.thumb
#else
.code 32
#endif
___
########################################################################
# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7
#
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
open TABLE,"<ecp_nistz256_table.c" or
open TABLE,"<${dir}../ecp_nistz256_table.c" or
die "failed to open ecp_nistz256_table.c:",$!;
use integer;
foreach(<TABLE>) {
s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo;
}
close TABLE;
# See ecp_nistz256_table.c for explanation for why it's 64*16*37.
# 64*16*37-1 is because $#arr returns last valid index or @arr, not
# amount of elements.
die "insane number of elements" if ($#arr != 64*16*37-1);
$code.=<<___;
.globl ecp_nistz256_precomputed
.type ecp_nistz256_precomputed,%object
.align 12
ecp_nistz256_precomputed:
___
########################################################################
# this conversion smashes P256_POINT_AFFINE by individual bytes with
# 64 byte interval, similar to
# 1111222233334444
# 1234123412341234
for(1..37) {
@tbl = splice(@arr,0,64*16);
for($i=0;$i<64;$i++) {
undef @line;
for($j=0;$j<64;$j++) {
push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff;
}
$code.=".byte\t";
$code.=join(',',map { sprintf "0x%02x",$_} @line);
$code.="\n";
}
}
$code.=<<___;
.size ecp_nistz256_precomputed,.-ecp_nistz256_precomputed
.align 5
.LRR: @ 2^512 mod P precomputed for NIST P256 polynomial
.long 0x00000003, 0x00000000, 0xffffffff, 0xfffffffb
.long 0xfffffffe, 0xffffffff, 0xfffffffd, 0x00000004
.Lone:
.long 1,0,0,0,0,0,0,0
.asciz "ECP_NISTZ256 for ARMv4, CRYPTOGAMS by <appro\@openssl.org>"
.align 6
___
########################################################################
# common register layout, note that $t2 is link register, so that if
# internal subroutine uses $t2, then it has to offload lr...
($r_ptr,$a_ptr,$b_ptr,$ff,$a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7,$t1,$t2)=
map("r$_",(0..12,14));
($t0,$t3)=($ff,$a_ptr);
$code.=<<___;
@ void ecp_nistz256_to_mont(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_to_mont
.type ecp_nistz256_to_mont,%function
ecp_nistz256_to_mont:
adr $b_ptr,.LRR
b .Lecp_nistz256_mul_mont
.size ecp_nistz256_to_mont,.-ecp_nistz256_to_mont
@ void ecp_nistz256_from_mont(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_from_mont
.type ecp_nistz256_from_mont,%function
ecp_nistz256_from_mont:
adr $b_ptr,.Lone
b .Lecp_nistz256_mul_mont
.size ecp_nistz256_from_mont,.-ecp_nistz256_from_mont
@ void ecp_nistz256_mul_by_2(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_mul_by_2
.type ecp_nistz256_mul_by_2,%function
.align 4
ecp_nistz256_mul_by_2:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_mul_by_2
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2
.type __ecp_nistz256_mul_by_2,%function
.align 4
__ecp_nistz256_mul_by_2:
ldr $a0,[$a_ptr,#0]
ldr $a1,[$a_ptr,#4]
ldr $a2,[$a_ptr,#8]
adds $a0,$a0,$a0 @ a[0:7]+=a[0:7], i.e. add with itself
ldr $a3,[$a_ptr,#12]
adcs $a1,$a1,$a1
ldr $a4,[$a_ptr,#16]
adcs $a2,$a2,$a2
ldr $a5,[$a_ptr,#20]
adcs $a3,$a3,$a3
ldr $a6,[$a_ptr,#24]
adcs $a4,$a4,$a4
ldr $a7,[$a_ptr,#28]
adcs $a5,$a5,$a5
adcs $a6,$a6,$a6
mov $ff,#0
adcs $a7,$a7,$a7
adc $ff,$ff,#0
b .Lreduce_by_sub
.size __ecp_nistz256_mul_by_2,.-__ecp_nistz256_mul_by_2
@ void ecp_nistz256_add(BN_ULONG r0[8],const BN_ULONG r1[8],
@ const BN_ULONG r2[8]);
.globl ecp_nistz256_add
.type ecp_nistz256_add,%function
.align 4
ecp_nistz256_add:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_add
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_add,.-ecp_nistz256_add
.type __ecp_nistz256_add,%function
.align 4
__ecp_nistz256_add:
str lr,[sp,#-4]! @ push lr
ldr $a0,[$a_ptr,#0]
ldr $a1,[$a_ptr,#4]
ldr $a2,[$a_ptr,#8]
ldr $a3,[$a_ptr,#12]
ldr $a4,[$a_ptr,#16]
ldr $t0,[$b_ptr,#0]
ldr $a5,[$a_ptr,#20]
ldr $t1,[$b_ptr,#4]
ldr $a6,[$a_ptr,#24]
ldr $t2,[$b_ptr,#8]
ldr $a7,[$a_ptr,#28]
ldr $t3,[$b_ptr,#12]
adds $a0,$a0,$t0
ldr $t0,[$b_ptr,#16]
adcs $a1,$a1,$t1
ldr $t1,[$b_ptr,#20]
adcs $a2,$a2,$t2
ldr $t2,[$b_ptr,#24]
adcs $a3,$a3,$t3
ldr $t3,[$b_ptr,#28]
adcs $a4,$a4,$t0
adcs $a5,$a5,$t1
adcs $a6,$a6,$t2
mov $ff,#0
adcs $a7,$a7,$t3
adc $ff,$ff,#0
ldr lr,[sp],#4 @ pop lr
.Lreduce_by_sub:
@ if a+b >= modulus, subtract modulus.
@
@ But since comparison implies subtraction, we subtract
@ modulus and then add it back if subraction borrowed.
subs $a0,$a0,#-1
sbcs $a1,$a1,#-1
sbcs $a2,$a2,#-1
sbcs $a3,$a3,#0
sbcs $a4,$a4,#0
sbcs $a5,$a5,#0
sbcs $a6,$a6,#1
sbcs $a7,$a7,#-1
sbc $ff,$ff,#0
@ Note that because mod has special form, i.e. consists of
@ 0xffffffff, 1 and 0s, we can conditionally synthesize it by
@ using value of borrow as a whole or extracting single bit.
@ Follow $ff register...
adds $a0,$a0,$ff @ add synthesized modulus
adcs $a1,$a1,$ff
str $a0,[$r_ptr,#0]
adcs $a2,$a2,$ff
str $a1,[$r_ptr,#4]
adcs $a3,$a3,#0
str $a2,[$r_ptr,#8]
adcs $a4,$a4,#0
str $a3,[$r_ptr,#12]
adcs $a5,$a5,#0
str $a4,[$r_ptr,#16]
adcs $a6,$a6,$ff,lsr#31
str $a5,[$r_ptr,#20]
adcs $a7,$a7,$ff
str $a6,[$r_ptr,#24]
str $a7,[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_add,.-__ecp_nistz256_add
@ void ecp_nistz256_mul_by_3(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_mul_by_3
.type ecp_nistz256_mul_by_3,%function
.align 4
ecp_nistz256_mul_by_3:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_mul_by_3
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3
.type __ecp_nistz256_mul_by_3,%function
.align 4
__ecp_nistz256_mul_by_3:
str lr,[sp,#-4]! @ push lr
@ As multiplication by 3 is performed as 2*n+n, below are inline
@ copies of __ecp_nistz256_mul_by_2 and __ecp_nistz256_add, see
@ corresponding subroutines for details.
ldr $a0,[$a_ptr,#0]
ldr $a1,[$a_ptr,#4]
ldr $a2,[$a_ptr,#8]
adds $a0,$a0,$a0 @ a[0:7]+=a[0:7]
ldr $a3,[$a_ptr,#12]
adcs $a1,$a1,$a1
ldr $a4,[$a_ptr,#16]
adcs $a2,$a2,$a2
ldr $a5,[$a_ptr,#20]
adcs $a3,$a3,$a3
ldr $a6,[$a_ptr,#24]
adcs $a4,$a4,$a4
ldr $a7,[$a_ptr,#28]
adcs $a5,$a5,$a5
adcs $a6,$a6,$a6
mov $ff,#0
adcs $a7,$a7,$a7
adc $ff,$ff,#0
subs $a0,$a0,#-1 @ .Lreduce_by_sub but without stores
sbcs $a1,$a1,#-1
sbcs $a2,$a2,#-1
sbcs $a3,$a3,#0
sbcs $a4,$a4,#0
sbcs $a5,$a5,#0
sbcs $a6,$a6,#1
sbcs $a7,$a7,#-1
sbc $ff,$ff,#0
adds $a0,$a0,$ff @ add synthesized modulus
adcs $a1,$a1,$ff
adcs $a2,$a2,$ff
adcs $a3,$a3,#0
adcs $a4,$a4,#0
ldr $b_ptr,[$a_ptr,#0]
adcs $a5,$a5,#0
ldr $t1,[$a_ptr,#4]
adcs $a6,$a6,$ff,lsr#31
ldr $t2,[$a_ptr,#8]
adc $a7,$a7,$ff
ldr $t0,[$a_ptr,#12]
adds $a0,$a0,$b_ptr @ 2*a[0:7]+=a[0:7]
ldr $b_ptr,[$a_ptr,#16]
adcs $a1,$a1,$t1
ldr $t1,[$a_ptr,#20]
adcs $a2,$a2,$t2
ldr $t2,[$a_ptr,#24]
adcs $a3,$a3,$t0
ldr $t3,[$a_ptr,#28]
adcs $a4,$a4,$b_ptr
adcs $a5,$a5,$t1
adcs $a6,$a6,$t2
mov $ff,#0
adcs $a7,$a7,$t3
adc $ff,$ff,#0
ldr lr,[sp],#4 @ pop lr
b .Lreduce_by_sub
.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3
@ void ecp_nistz256_div_by_2(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_div_by_2
.type ecp_nistz256_div_by_2,%function
.align 4
ecp_nistz256_div_by_2:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_div_by_2
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2
.type __ecp_nistz256_div_by_2,%function
.align 4
__ecp_nistz256_div_by_2:
@ ret = (a is odd ? a+mod : a) >> 1
ldr $a0,[$a_ptr,#0]
ldr $a1,[$a_ptr,#4]
ldr $a2,[$a_ptr,#8]
mov $ff,$a0,lsl#31 @ place least significant bit to most
@ significant position, now arithmetic
@ right shift by 31 will produce -1 or
@ 0, while logical right shift 1 or 0,
@ this is how modulus is conditionally
@ synthesized in this case...
ldr $a3,[$a_ptr,#12]
adds $a0,$a0,$ff,asr#31
ldr $a4,[$a_ptr,#16]
adcs $a1,$a1,$ff,asr#31
ldr $a5,[$a_ptr,#20]
adcs $a2,$a2,$ff,asr#31
ldr $a6,[$a_ptr,#24]
adcs $a3,$a3,#0
ldr $a7,[$a_ptr,#28]
adcs $a4,$a4,#0
mov $a0,$a0,lsr#1 @ a[0:7]>>=1, we can start early
@ because it doesn't affect flags
adcs $a5,$a5,#0
orr $a0,$a0,$a1,lsl#31
adcs $a6,$a6,$ff,lsr#31
mov $b_ptr,#0
adcs $a7,$a7,$ff,asr#31
mov $a1,$a1,lsr#1
adc $b_ptr,$b_ptr,#0 @ top-most carry bit from addition
orr $a1,$a1,$a2,lsl#31
mov $a2,$a2,lsr#1
str $a0,[$r_ptr,#0]
orr $a2,$a2,$a3,lsl#31
mov $a3,$a3,lsr#1
str $a1,[$r_ptr,#4]
orr $a3,$a3,$a4,lsl#31
mov $a4,$a4,lsr#1
str $a2,[$r_ptr,#8]
orr $a4,$a4,$a5,lsl#31
mov $a5,$a5,lsr#1
str $a3,[$r_ptr,#12]
orr $a5,$a5,$a6,lsl#31
mov $a6,$a6,lsr#1
str $a4,[$r_ptr,#16]
orr $a6,$a6,$a7,lsl#31
mov $a7,$a7,lsr#1
str $a5,[$r_ptr,#20]
orr $a7,$a7,$b_ptr,lsl#31 @ don't forget the top-most carry bit
str $a6,[$r_ptr,#24]
str $a7,[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_div_by_2,.-__ecp_nistz256_div_by_2
@ void ecp_nistz256_sub(BN_ULONG r0[8],const BN_ULONG r1[8],
@ const BN_ULONG r2[8]);
.globl ecp_nistz256_sub
.type ecp_nistz256_sub,%function
.align 4
ecp_nistz256_sub:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_sub
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_sub,.-ecp_nistz256_sub
.type __ecp_nistz256_sub,%function
.align 4
__ecp_nistz256_sub:
str lr,[sp,#-4]! @ push lr
ldr $a0,[$a_ptr,#0]
ldr $a1,[$a_ptr,#4]
ldr $a2,[$a_ptr,#8]
ldr $a3,[$a_ptr,#12]
ldr $a4,[$a_ptr,#16]
ldr $t0,[$b_ptr,#0]
ldr $a5,[$a_ptr,#20]
ldr $t1,[$b_ptr,#4]
ldr $a6,[$a_ptr,#24]
ldr $t2,[$b_ptr,#8]
ldr $a7,[$a_ptr,#28]
ldr $t3,[$b_ptr,#12]
subs $a0,$a0,$t0
ldr $t0,[$b_ptr,#16]
sbcs $a1,$a1,$t1
ldr $t1,[$b_ptr,#20]
sbcs $a2,$a2,$t2
ldr $t2,[$b_ptr,#24]
sbcs $a3,$a3,$t3
ldr $t3,[$b_ptr,#28]
sbcs $a4,$a4,$t0
sbcs $a5,$a5,$t1
sbcs $a6,$a6,$t2
sbcs $a7,$a7,$t3
sbc $ff,$ff,$ff @ broadcast borrow bit
ldr lr,[sp],#4 @ pop lr
.Lreduce_by_add:
@ if a-b borrows, add modulus.
@
@ Note that because mod has special form, i.e. consists of
@ 0xffffffff, 1 and 0s, we can conditionally synthesize it by
@ broadcasting borrow bit to a register, $ff, and using it as
@ a whole or extracting single bit.
adds $a0,$a0,$ff @ add synthesized modulus
adcs $a1,$a1,$ff
str $a0,[$r_ptr,#0]
adcs $a2,$a2,$ff
str $a1,[$r_ptr,#4]
adcs $a3,$a3,#0
str $a2,[$r_ptr,#8]
adcs $a4,$a4,#0
str $a3,[$r_ptr,#12]
adcs $a5,$a5,#0
str $a4,[$r_ptr,#16]
adcs $a6,$a6,$ff,lsr#31
str $a5,[$r_ptr,#20]
adcs $a7,$a7,$ff
str $a6,[$r_ptr,#24]
str $a7,[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_sub,.-__ecp_nistz256_sub
@ void ecp_nistz256_neg(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_neg
.type ecp_nistz256_neg,%function
.align 4
ecp_nistz256_neg:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_neg
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_neg,.-ecp_nistz256_neg
.type __ecp_nistz256_neg,%function
.align 4
__ecp_nistz256_neg:
ldr $a0,[$a_ptr,#0]
eor $ff,$ff,$ff
ldr $a1,[$a_ptr,#4]
ldr $a2,[$a_ptr,#8]
subs $a0,$ff,$a0
ldr $a3,[$a_ptr,#12]
sbcs $a1,$ff,$a1
ldr $a4,[$a_ptr,#16]
sbcs $a2,$ff,$a2
ldr $a5,[$a_ptr,#20]
sbcs $a3,$ff,$a3
ldr $a6,[$a_ptr,#24]
sbcs $a4,$ff,$a4
ldr $a7,[$a_ptr,#28]
sbcs $a5,$ff,$a5
sbcs $a6,$ff,$a6
sbcs $a7,$ff,$a7
sbc $ff,$ff,$ff
b .Lreduce_by_add
.size __ecp_nistz256_neg,.-__ecp_nistz256_neg
___
{
my @acc=map("r$_",(3..11));
my ($t0,$t1,$bj,$t2,$t3)=map("r$_",(0,1,2,12,14));
$code.=<<___;
@ void ecp_nistz256_sqr_mont(BN_ULONG r0[8],const BN_ULONG r1[8]);
.globl ecp_nistz256_sqr_mont
.type ecp_nistz256_sqr_mont,%function
.align 4
ecp_nistz256_sqr_mont:
mov $b_ptr,$a_ptr
b .Lecp_nistz256_mul_mont
.size ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont
@ void ecp_nistz256_mul_mont(BN_ULONG r0[8],const BN_ULONG r1[8],
@ const BN_ULONG r2[8]);
.globl ecp_nistz256_mul_mont
.type ecp_nistz256_mul_mont,%function
.align 4
ecp_nistz256_mul_mont:
.Lecp_nistz256_mul_mont:
stmdb sp!,{r4-r12,lr}
bl __ecp_nistz256_mul_mont
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont
.type __ecp_nistz256_mul_mont,%function
.align 4
__ecp_nistz256_mul_mont:
stmdb sp!,{r0-r2,lr} @ make a copy of arguments too
ldr $bj,[$b_ptr,#0] @ b[0]
ldmia $a_ptr,{@acc[1]-@acc[8]}
umull @acc[0],$t3,@acc[1],$bj @ r[0]=a[0]*b[0]
stmdb sp!,{$acc[1]-@acc[8]} @ copy a[0-7] to stack, so
@ that it can be addressed
@ without spending register
@ on address
umull @acc[1],$t0,@acc[2],$bj @ r[1]=a[1]*b[0]
umull @acc[2],$t1,@acc[3],$bj
adds @acc[1],@acc[1],$t3 @ accumulate high part of mult
umull @acc[3],$t2,@acc[4],$bj
adcs @acc[2],@acc[2],$t0
umull @acc[4],$t3,@acc[5],$bj
adcs @acc[3],@acc[3],$t1
umull @acc[5],$t0,@acc[6],$bj
adcs @acc[4],@acc[4],$t2
umull @acc[6],$t1,@acc[7],$bj
adcs @acc[5],@acc[5],$t3
umull @acc[7],$t2,@acc[8],$bj
adcs @acc[6],@acc[6],$t0
adcs @acc[7],@acc[7],$t1
eor $t3,$t3,$t3 @ first overflow bit is zero
adc @acc[8],$t2,#0
___
for(my $i=1;$i<8;$i++) {
my $t4=@acc[0];
# Reduction iteration is normally performed by accumulating
# result of multiplication of modulus by "magic" digit [and
# omitting least significant word, which is guaranteed to
# be 0], but thanks to special form of modulus and "magic"
# digit being equal to least significant word, it can be
# performed with additions and subtractions alone. Indeed:
#
# ffff.0001.0000.0000.0000.ffff.ffff.ffff
# * abcd
# + xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd
#
# Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we
# rewrite above as:
#
# xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd
# + abcd.0000.abcd.0000.0000.abcd.0000.0000.0000
# - abcd.0000.0000.0000.0000.0000.0000.abcd
#
# or marking redundant operations:
#
# xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.----
# + abcd.0000.abcd.0000.0000.abcd.----.----.----
# - abcd.----.----.----.----.----.----.----
$code.=<<___;
@ multiplication-less reduction $i
adds @acc[3],@acc[3],@acc[0] @ r[3]+=r[0]
ldr $bj,[sp,#40] @ restore b_ptr
adcs @acc[4],@acc[4],#0 @ r[4]+=0
adcs @acc[5],@acc[5],#0 @ r[5]+=0
adcs @acc[6],@acc[6],@acc[0] @ r[6]+=r[0]
ldr $t1,[sp,#0] @ load a[0]
adcs @acc[7],@acc[7],#0 @ r[7]+=0
ldr $bj,[$bj,#4*$i] @ load b[i]
adcs @acc[8],@acc[8],@acc[0] @ r[8]+=r[0]
eor $t0,$t0,$t0
adc $t3,$t3,#0 @ overflow bit
subs @acc[7],@acc[7],@acc[0] @ r[7]-=r[0]
ldr $t2,[sp,#4] @ a[1]
sbcs @acc[8],@acc[8],#0 @ r[8]-=0
umlal @acc[1],$t0,$t1,$bj @ "r[0]"+=a[0]*b[i]
eor $t1,$t1,$t1
sbc @acc[0],$t3,#0 @ overflow bit, keep in mind
@ that netto result is
@ addition of a value which
@ makes underflow impossible
ldr $t3,[sp,#8] @ a[2]
umlal @acc[2],$t1,$t2,$bj @ "r[1]"+=a[1]*b[i]
str @acc[0],[sp,#36] @ temporarily offload overflow
eor $t2,$t2,$t2
ldr $t4,[sp,#12] @ a[3], $t4 is alias @acc[0]
umlal @acc[3],$t2,$t3,$bj @ "r[2]"+=a[2]*b[i]
eor $t3,$t3,$t3
adds @acc[2],@acc[2],$t0 @ accumulate high part of mult
ldr $t0,[sp,#16] @ a[4]
umlal @acc[4],$t3,$t4,$bj @ "r[3]"+=a[3]*b[i]
eor $t4,$t4,$t4
adcs @acc[3],@acc[3],$t1
ldr $t1,[sp,#20] @ a[5]
umlal @acc[5],$t4,$t0,$bj @ "r[4]"+=a[4]*b[i]
eor $t0,$t0,$t0
adcs @acc[4],@acc[4],$t2
ldr $t2,[sp,#24] @ a[6]
umlal @acc[6],$t0,$t1,$bj @ "r[5]"+=a[5]*b[i]
eor $t1,$t1,$t1
adcs @acc[5],@acc[5],$t3
ldr $t3,[sp,#28] @ a[7]
umlal @acc[7],$t1,$t2,$bj @ "r[6]"+=a[6]*b[i]
eor $t2,$t2,$t2
adcs @acc[6],@acc[6],$t4
ldr @acc[0],[sp,#36] @ restore overflow bit
umlal @acc[8],$t2,$t3,$bj @ "r[7]"+=a[7]*b[i]
eor $t3,$t3,$t3
adcs @acc[7],@acc[7],$t0
adcs @acc[8],@acc[8],$t1
adcs @acc[0],$acc[0],$t2
adc $t3,$t3,#0 @ new overflow bit
___
push(@acc,shift(@acc)); # rotate registers, so that
# "r[i]" becomes r[i]
}
$code.=<<___;
@ last multiplication-less reduction
adds @acc[3],@acc[3],@acc[0]
ldr $r_ptr,[sp,#32] @ restore r_ptr
adcs @acc[4],@acc[4],#0
adcs @acc[5],@acc[5],#0
adcs @acc[6],@acc[6],@acc[0]
adcs @acc[7],@acc[7],#0
adcs @acc[8],@acc[8],@acc[0]
adc $t3,$t3,#0
subs @acc[7],@acc[7],@acc[0]
sbcs @acc[8],@acc[8],#0
sbc @acc[0],$t3,#0 @ overflow bit
@ Final step is "if result > mod, subtract mod", but we do it
@ "other way around", namely subtract modulus from result
@ and if it borrowed, add modulus back.
adds @acc[1],@acc[1],#1 @ subs @acc[1],@acc[1],#-1
adcs @acc[2],@acc[2],#0 @ sbcs @acc[2],@acc[2],#-1
adcs @acc[3],@acc[3],#0 @ sbcs @acc[3],@acc[3],#-1
sbcs @acc[4],@acc[4],#0
sbcs @acc[5],@acc[5],#0
sbcs @acc[6],@acc[6],#0
sbcs @acc[7],@acc[7],#1
adcs @acc[8],@acc[8],#0 @ sbcs @acc[8],@acc[8],#-1
ldr lr,[sp,#44] @ restore lr
sbc @acc[0],@acc[0],#0 @ broadcast borrow bit
add sp,sp,#48
@ Note that because mod has special form, i.e. consists of
@ 0xffffffff, 1 and 0s, we can conditionally synthesize it by
@ broadcasting borrow bit to a register, @acc[0], and using it as
@ a whole or extracting single bit.
adds @acc[1],@acc[1],@acc[0] @ add modulus or zero
adcs @acc[2],@acc[2],@acc[0]
str @acc[1],[$r_ptr,#0]
adcs @acc[3],@acc[3],@acc[0]
str @acc[2],[$r_ptr,#4]
adcs @acc[4],@acc[4],#0
str @acc[3],[$r_ptr,#8]
adcs @acc[5],@acc[5],#0
str @acc[4],[$r_ptr,#12]
adcs @acc[6],@acc[6],#0
str @acc[5],[$r_ptr,#16]
adcs @acc[7],@acc[7],@acc[0],lsr#31
str @acc[6],[$r_ptr,#20]
adc @acc[8],@acc[8],@acc[0]
str @acc[7],[$r_ptr,#24]
str @acc[8],[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_mul_mont,.-__ecp_nistz256_mul_mont
___
}
{
my ($out,$inp,$index,$mask)=map("r$_",(0..3));
$code.=<<___;
@ void ecp_nistz256_scatter_w5(void *r0,const P256_POINT *r1,
@ int r2);
.globl ecp_nistz256_scatter_w5
.type ecp_nistz256_scatter_w5,%function
.align 5
ecp_nistz256_scatter_w5:
stmdb sp!,{r4-r11}
add $out,$out,$index,lsl#2
ldmia $inp!,{r4-r11} @ X
str r4,[$out,#64*0-4]
str r5,[$out,#64*1-4]
str r6,[$out,#64*2-4]
str r7,[$out,#64*3-4]
str r8,[$out,#64*4-4]
str r9,[$out,#64*5-4]
str r10,[$out,#64*6-4]
str r11,[$out,#64*7-4]
add $out,$out,#64*8
ldmia $inp!,{r4-r11} @ Y
str r4,[$out,#64*0-4]
str r5,[$out,#64*1-4]
str r6,[$out,#64*2-4]
str r7,[$out,#64*3-4]
str r8,[$out,#64*4-4]
str r9,[$out,#64*5-4]
str r10,[$out,#64*6-4]
str r11,[$out,#64*7-4]
add $out,$out,#64*8
ldmia $inp,{r4-r11} @ Z
str r4,[$out,#64*0-4]
str r5,[$out,#64*1-4]
str r6,[$out,#64*2-4]
str r7,[$out,#64*3-4]
str r8,[$out,#64*4-4]
str r9,[$out,#64*5-4]
str r10,[$out,#64*6-4]
str r11,[$out,#64*7-4]
ldmia sp!,{r4-r11}
#if __ARM_ARCH__>=5 || defined(__thumb__)
bx lr
#else
mov pc,lr
#endif
.size ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5
@ void ecp_nistz256_gather_w5(P256_POINT *r0,const void *r1,
@ int r2);
.globl ecp_nistz256_gather_w5
.type ecp_nistz256_gather_w5,%function
.align 5
ecp_nistz256_gather_w5:
stmdb sp!,{r4-r11}
cmp $index,#0
mov $mask,#0
#ifdef __thumb2__
itt ne
#endif
subne $index,$index,#1
movne $mask,#-1
add $inp,$inp,$index,lsl#2
ldr r4,[$inp,#64*0]
ldr r5,[$inp,#64*1]
ldr r6,[$inp,#64*2]
and r4,r4,$mask
ldr r7,[$inp,#64*3]
and r5,r5,$mask
ldr r8,[$inp,#64*4]
and r6,r6,$mask
ldr r9,[$inp,#64*5]
and r7,r7,$mask
ldr r10,[$inp,#64*6]
and r8,r8,$mask
ldr r11,[$inp,#64*7]
add $inp,$inp,#64*8
and r9,r9,$mask
and r10,r10,$mask
and r11,r11,$mask
stmia $out!,{r4-r11} @ X
ldr r4,[$inp,#64*0]
ldr r5,[$inp,#64*1]
ldr r6,[$inp,#64*2]
and r4,r4,$mask
ldr r7,[$inp,#64*3]
and r5,r5,$mask
ldr r8,[$inp,#64*4]
and r6,r6,$mask
ldr r9,[$inp,#64*5]
and r7,r7,$mask
ldr r10,[$inp,#64*6]
and r8,r8,$mask
ldr r11,[$inp,#64*7]
add $inp,$inp,#64*8
and r9,r9,$mask
and r10,r10,$mask
and r11,r11,$mask
stmia $out!,{r4-r11} @ Y
ldr r4,[$inp,#64*0]
ldr r5,[$inp,#64*1]
ldr r6,[$inp,#64*2]
and r4,r4,$mask
ldr r7,[$inp,#64*3]
and r5,r5,$mask
ldr r8,[$inp,#64*4]
and r6,r6,$mask
ldr r9,[$inp,#64*5]
and r7,r7,$mask
ldr r10,[$inp,#64*6]
and r8,r8,$mask
ldr r11,[$inp,#64*7]
and r9,r9,$mask
and r10,r10,$mask
and r11,r11,$mask
stmia $out,{r4-r11} @ Z
ldmia sp!,{r4-r11}
#if __ARM_ARCH__>=5 || defined(__thumb__)
bx lr
#else
mov pc,lr
#endif
.size ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5
@ void ecp_nistz256_scatter_w7(void *r0,const P256_POINT_AFFINE *r1,
@ int r2);
.globl ecp_nistz256_scatter_w7
.type ecp_nistz256_scatter_w7,%function
.align 5
ecp_nistz256_scatter_w7:
add $out,$out,$index
mov $index,#64/4
.Loop_scatter_w7:
ldr $mask,[$inp],#4
subs $index,$index,#1
strb $mask,[$out,#64*0-1]
mov $mask,$mask,lsr#8
strb $mask,[$out,#64*1-1]
mov $mask,$mask,lsr#8
strb $mask,[$out,#64*2-1]
mov $mask,$mask,lsr#8
strb $mask,[$out,#64*3-1]
add $out,$out,#64*4
bne .Loop_scatter_w7
#if __ARM_ARCH__>=5 || defined(__thumb__)
bx lr
#else
mov pc,lr
#endif
.size ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7
@ void ecp_nistz256_gather_w7(P256_POINT_AFFINE *r0,const void *r1,
@ int r2);
.globl ecp_nistz256_gather_w7
.type ecp_nistz256_gather_w7,%function
.align 5
ecp_nistz256_gather_w7:
stmdb sp!,{r4-r7}
cmp $index,#0
mov $mask,#0
#ifdef __thumb2__
itt ne
#endif
subne $index,$index,#1
movne $mask,#-1
add $inp,$inp,$index
mov $index,#64/4
nop
.Loop_gather_w7:
ldrb r4,[$inp,#64*0]
subs $index,$index,#1
ldrb r5,[$inp,#64*1]
ldrb r6,[$inp,#64*2]
ldrb r7,[$inp,#64*3]
add $inp,$inp,#64*4
orr r4,r4,r5,lsl#8
orr r4,r4,r6,lsl#16
orr r4,r4,r7,lsl#24
and r4,r4,$mask
str r4,[$out],#4
bne .Loop_gather_w7
ldmia sp!,{r4-r7}
#if __ARM_ARCH__>=5 || defined(__thumb__)
bx lr
#else
mov pc,lr
#endif
.size ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7
___
}
if (0) {
# In comparison to integer-only equivalent of below subroutine:
#
# Cortex-A8 +10%
# Cortex-A9 -10%
# Snapdragon S4 +5%
#
# As not all time is spent in multiplication, overall impact is deemed
# too low to care about.
my ($A0,$A1,$A2,$A3,$Bi,$zero,$temp)=map("d$_",(0..7));
my $mask="q4";
my $mult="q5";
my @AxB=map("q$_",(8..15));
my ($rptr,$aptr,$bptr,$toutptr)=map("r$_",(0..3));
$code.=<<___;
#if __ARM_ARCH__>=7
.fpu neon
.globl ecp_nistz256_mul_mont_neon
.type ecp_nistz256_mul_mont_neon,%function
.align 5
ecp_nistz256_mul_mont_neon:
mov ip,sp
stmdb sp!,{r4-r9}
vstmdb sp!,{q4-q5} @ ABI specification says so
sub $toutptr,sp,#40
vld1.32 {${Bi}[0]},[$bptr,:32]!
veor $zero,$zero,$zero
vld1.32 {$A0-$A3}, [$aptr] @ can't specify :32 :-(
vzip.16 $Bi,$zero
mov sp,$toutptr @ alloca
vmov.i64 $mask,#0xffff
vmull.u32 @AxB[0],$Bi,${A0}[0]
vmull.u32 @AxB[1],$Bi,${A0}[1]
vmull.u32 @AxB[2],$Bi,${A1}[0]
vmull.u32 @AxB[3],$Bi,${A1}[1]
vshr.u64 $temp,@AxB[0]#lo,#16
vmull.u32 @AxB[4],$Bi,${A2}[0]
vadd.u64 @AxB[0]#hi,@AxB[0]#hi,$temp
vmull.u32 @AxB[5],$Bi,${A2}[1]
vshr.u64 $temp,@AxB[0]#hi,#16 @ upper 32 bits of a[0]*b[0]
vmull.u32 @AxB[6],$Bi,${A3}[0]
vand.u64 @AxB[0],@AxB[0],$mask @ lower 32 bits of a[0]*b[0]
vmull.u32 @AxB[7],$Bi,${A3}[1]
___
for($i=1;$i<8;$i++) {
$code.=<<___;
vld1.32 {${Bi}[0]},[$bptr,:32]!
veor $zero,$zero,$zero
vadd.u64 @AxB[1]#lo,@AxB[1]#lo,$temp @ reduction
vshl.u64 $mult,@AxB[0],#32
vadd.u64 @AxB[3],@AxB[3],@AxB[0]
vsub.u64 $mult,$mult,@AxB[0]
vzip.16 $Bi,$zero
vadd.u64 @AxB[6],@AxB[6],@AxB[0]
vadd.u64 @AxB[7],@AxB[7],$mult
___
push(@AxB,shift(@AxB));
$code.=<<___;
vmlal.u32 @AxB[0],$Bi,${A0}[0]
vmlal.u32 @AxB[1],$Bi,${A0}[1]
vmlal.u32 @AxB[2],$Bi,${A1}[0]
vmlal.u32 @AxB[3],$Bi,${A1}[1]
vshr.u64 $temp,@AxB[0]#lo,#16
vmlal.u32 @AxB[4],$Bi,${A2}[0]
vadd.u64 @AxB[0]#hi,@AxB[0]#hi,$temp
vmlal.u32 @AxB[5],$Bi,${A2}[1]
vshr.u64 $temp,@AxB[0]#hi,#16 @ upper 33 bits of a[0]*b[i]+t[0]
vmlal.u32 @AxB[6],$Bi,${A3}[0]
vand.u64 @AxB[0],@AxB[0],$mask @ lower 32 bits of a[0]*b[0]
vmull.u32 @AxB[7],$Bi,${A3}[1]
___
}
$code.=<<___;
vadd.u64 @AxB[1]#lo,@AxB[1]#lo,$temp @ last reduction
vshl.u64 $mult,@AxB[0],#32
vadd.u64 @AxB[3],@AxB[3],@AxB[0]
vsub.u64 $mult,$mult,@AxB[0]
vadd.u64 @AxB[6],@AxB[6],@AxB[0]
vadd.u64 @AxB[7],@AxB[7],$mult
vshr.u64 $temp,@AxB[1]#lo,#16 @ convert
vadd.u64 @AxB[1]#hi,@AxB[1]#hi,$temp
vshr.u64 $temp,@AxB[1]#hi,#16
vzip.16 @AxB[1]#lo,@AxB[1]#hi
___
foreach (2..7) {
$code.=<<___;
vadd.u64 @AxB[$_]#lo,@AxB[$_]#lo,$temp
vst1.32 {@AxB[$_-1]#lo[0]},[$toutptr,:32]!
vshr.u64 $temp,@AxB[$_]#lo,#16
vadd.u64 @AxB[$_]#hi,@AxB[$_]#hi,$temp
vshr.u64 $temp,@AxB[$_]#hi,#16
vzip.16 @AxB[$_]#lo,@AxB[$_]#hi
___
}
$code.=<<___;
vst1.32 {@AxB[7]#lo[0]},[$toutptr,:32]!
vst1.32 {$temp},[$toutptr] @ upper 33 bits
ldr r1,[sp,#0]
ldr r2,[sp,#4]
ldr r3,[sp,#8]
subs r1,r1,#-1
ldr r4,[sp,#12]
sbcs r2,r2,#-1
ldr r5,[sp,#16]
sbcs r3,r3,#-1
ldr r6,[sp,#20]
sbcs r4,r4,#0
ldr r7,[sp,#24]
sbcs r5,r5,#0
ldr r8,[sp,#28]
sbcs r6,r6,#0
ldr r9,[sp,#32] @ top-most bit
sbcs r7,r7,#1
sub sp,ip,#40+16
sbcs r8,r8,#-1
sbc r9,r9,#0
vldmia sp!,{q4-q5}
adds r1,r1,r9
adcs r2,r2,r9
str r1,[$rptr,#0]
adcs r3,r3,r9
str r2,[$rptr,#4]
adcs r4,r4,#0
str r3,[$rptr,#8]
adcs r5,r5,#0
str r4,[$rptr,#12]
adcs r6,r6,#0
str r5,[$rptr,#16]
adcs r7,r7,r9,lsr#31
str r6,[$rptr,#20]
adcs r8,r8,r9
str r7,[$rptr,#24]
str r8,[$rptr,#28]
ldmia sp!,{r4-r9}
bx lr
.size ecp_nistz256_mul_mont_neon,.-ecp_nistz256_mul_mont_neon
#endif
___
}
{{{
########################################################################
# Below $aN assignment matches order in which 256-bit result appears in
# register bank at return from __ecp_nistz256_mul_mont, so that we can
# skip over reloading it from memory. This means that below functions
# use custom calling sequence accepting 256-bit input in registers,
# output pointer in r0, $r_ptr, and optional pointer in r2, $b_ptr.
#
# See their "normal" counterparts for insights on calculations.
my ($a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7,
$t0,$t1,$t2,$t3)=map("r$_",(11,3..10,12,14,1));
my $ff=$b_ptr;
$code.=<<___;
.type __ecp_nistz256_sub_from,%function
.align 5
__ecp_nistz256_sub_from:
str lr,[sp,#-4]! @ push lr
ldr $t0,[$b_ptr,#0]
ldr $t1,[$b_ptr,#4]
ldr $t2,[$b_ptr,#8]
ldr $t3,[$b_ptr,#12]
subs $a0,$a0,$t0
ldr $t0,[$b_ptr,#16]
sbcs $a1,$a1,$t1
ldr $t1,[$b_ptr,#20]
sbcs $a2,$a2,$t2
ldr $t2,[$b_ptr,#24]
sbcs $a3,$a3,$t3
ldr $t3,[$b_ptr,#28]
sbcs $a4,$a4,$t0
sbcs $a5,$a5,$t1
sbcs $a6,$a6,$t2
sbcs $a7,$a7,$t3
sbc $ff,$ff,$ff @ broadcast borrow bit
ldr lr,[sp],#4 @ pop lr
adds $a0,$a0,$ff @ add synthesized modulus
adcs $a1,$a1,$ff
str $a0,[$r_ptr,#0]
adcs $a2,$a2,$ff
str $a1,[$r_ptr,#4]
adcs $a3,$a3,#0
str $a2,[$r_ptr,#8]
adcs $a4,$a4,#0
str $a3,[$r_ptr,#12]
adcs $a5,$a5,#0
str $a4,[$r_ptr,#16]
adcs $a6,$a6,$ff,lsr#31
str $a5,[$r_ptr,#20]
adcs $a7,$a7,$ff
str $a6,[$r_ptr,#24]
str $a7,[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_sub_from,.-__ecp_nistz256_sub_from
.type __ecp_nistz256_sub_morf,%function
.align 5
__ecp_nistz256_sub_morf:
str lr,[sp,#-4]! @ push lr
ldr $t0,[$b_ptr,#0]
ldr $t1,[$b_ptr,#4]
ldr $t2,[$b_ptr,#8]
ldr $t3,[$b_ptr,#12]
subs $a0,$t0,$a0
ldr $t0,[$b_ptr,#16]
sbcs $a1,$t1,$a1
ldr $t1,[$b_ptr,#20]
sbcs $a2,$t2,$a2
ldr $t2,[$b_ptr,#24]
sbcs $a3,$t3,$a3
ldr $t3,[$b_ptr,#28]
sbcs $a4,$t0,$a4
sbcs $a5,$t1,$a5
sbcs $a6,$t2,$a6
sbcs $a7,$t3,$a7
sbc $ff,$ff,$ff @ broadcast borrow bit
ldr lr,[sp],#4 @ pop lr
adds $a0,$a0,$ff @ add synthesized modulus
adcs $a1,$a1,$ff
str $a0,[$r_ptr,#0]
adcs $a2,$a2,$ff
str $a1,[$r_ptr,#4]
adcs $a3,$a3,#0
str $a2,[$r_ptr,#8]
adcs $a4,$a4,#0
str $a3,[$r_ptr,#12]
adcs $a5,$a5,#0
str $a4,[$r_ptr,#16]
adcs $a6,$a6,$ff,lsr#31
str $a5,[$r_ptr,#20]
adcs $a7,$a7,$ff
str $a6,[$r_ptr,#24]
str $a7,[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_sub_morf,.-__ecp_nistz256_sub_morf
.type __ecp_nistz256_add_self,%function
.align 4
__ecp_nistz256_add_self:
adds $a0,$a0,$a0 @ a[0:7]+=a[0:7]
adcs $a1,$a1,$a1
adcs $a2,$a2,$a2
adcs $a3,$a3,$a3
adcs $a4,$a4,$a4
adcs $a5,$a5,$a5
adcs $a6,$a6,$a6
mov $ff,#0
adcs $a7,$a7,$a7
adc $ff,$ff,#0
@ if a+b >= modulus, subtract modulus.
@
@ But since comparison implies subtraction, we subtract
@ modulus and then add it back if subraction borrowed.
subs $a0,$a0,#-1
sbcs $a1,$a1,#-1
sbcs $a2,$a2,#-1
sbcs $a3,$a3,#0
sbcs $a4,$a4,#0
sbcs $a5,$a5,#0
sbcs $a6,$a6,#1
sbcs $a7,$a7,#-1
sbc $ff,$ff,#0
@ Note that because mod has special form, i.e. consists of
@ 0xffffffff, 1 and 0s, we can conditionally synthesize it by
@ using value of borrow as a whole or extracting single bit.
@ Follow $ff register...
adds $a0,$a0,$ff @ add synthesized modulus
adcs $a1,$a1,$ff
str $a0,[$r_ptr,#0]
adcs $a2,$a2,$ff
str $a1,[$r_ptr,#4]
adcs $a3,$a3,#0
str $a2,[$r_ptr,#8]
adcs $a4,$a4,#0
str $a3,[$r_ptr,#12]
adcs $a5,$a5,#0
str $a4,[$r_ptr,#16]
adcs $a6,$a6,$ff,lsr#31
str $a5,[$r_ptr,#20]
adcs $a7,$a7,$ff
str $a6,[$r_ptr,#24]
str $a7,[$r_ptr,#28]
mov pc,lr
.size __ecp_nistz256_add_self,.-__ecp_nistz256_add_self
___
########################################################################
# following subroutines are "literal" implementation of those found in
# ecp_nistz256.c
#
########################################################################
# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp);
#
{
my ($S,$M,$Zsqr,$in_x,$tmp0)=map(32*$_,(0..4));
# above map() describes stack layout with 5 temporary
# 256-bit vectors on top. Then note that we push
# starting from r0, which means that we have copy of
# input arguments just below these temporary vectors.
$code.=<<___;
.globl ecp_nistz256_point_double
.type ecp_nistz256_point_double,%function
.align 5
ecp_nistz256_point_double:
stmdb sp!,{r0-r12,lr} @ push from r0, unusual, but intentional
sub sp,sp,#32*5
.Lpoint_double_shortcut:
add r3,sp,#$in_x
ldmia $a_ptr!,{r4-r11} @ copy in_x
stmia r3,{r4-r11}
add $r_ptr,sp,#$S
bl __ecp_nistz256_mul_by_2 @ p256_mul_by_2(S, in_y);
add $b_ptr,$a_ptr,#32
add $a_ptr,$a_ptr,#32
add $r_ptr,sp,#$Zsqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Zsqr, in_z);
add $a_ptr,sp,#$S
add $b_ptr,sp,#$S
add $r_ptr,sp,#$S
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(S, S);
ldr $b_ptr,[sp,#32*5+4]
add $a_ptr,$b_ptr,#32
add $b_ptr,$b_ptr,#64
add $r_ptr,sp,#$tmp0
bl __ecp_nistz256_mul_mont @ p256_mul_mont(tmp0, in_z, in_y);
ldr $r_ptr,[sp,#32*5]
add $r_ptr,$r_ptr,#64
bl __ecp_nistz256_add_self @ p256_mul_by_2(res_z, tmp0);
add $a_ptr,sp,#$in_x
add $b_ptr,sp,#$Zsqr
add $r_ptr,sp,#$M
bl __ecp_nistz256_add @ p256_add(M, in_x, Zsqr);
add $a_ptr,sp,#$in_x
add $b_ptr,sp,#$Zsqr
add $r_ptr,sp,#$Zsqr
bl __ecp_nistz256_sub @ p256_sub(Zsqr, in_x, Zsqr);
add $a_ptr,sp,#$S
add $b_ptr,sp,#$S
add $r_ptr,sp,#$tmp0
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(tmp0, S);
add $a_ptr,sp,#$Zsqr
add $b_ptr,sp,#$M
add $r_ptr,sp,#$M
bl __ecp_nistz256_mul_mont @ p256_mul_mont(M, M, Zsqr);
ldr $r_ptr,[sp,#32*5]
add $a_ptr,sp,#$tmp0
add $r_ptr,$r_ptr,#32
bl __ecp_nistz256_div_by_2 @ p256_div_by_2(res_y, tmp0);
add $a_ptr,sp,#$M
add $r_ptr,sp,#$M
bl __ecp_nistz256_mul_by_3 @ p256_mul_by_3(M, M);
add $a_ptr,sp,#$in_x
add $b_ptr,sp,#$S
add $r_ptr,sp,#$S
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S, S, in_x);
add $r_ptr,sp,#$tmp0
bl __ecp_nistz256_add_self @ p256_mul_by_2(tmp0, S);
ldr $r_ptr,[sp,#32*5]
add $a_ptr,sp,#$M
add $b_ptr,sp,#$M
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(res_x, M);
add $b_ptr,sp,#$tmp0
bl __ecp_nistz256_sub_from @ p256_sub(res_x, res_x, tmp0);
add $b_ptr,sp,#$S
add $r_ptr,sp,#$S
bl __ecp_nistz256_sub_morf @ p256_sub(S, S, res_x);
add $a_ptr,sp,#$M
add $b_ptr,sp,#$S
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S, S, M);
ldr $r_ptr,[sp,#32*5]
add $b_ptr,$r_ptr,#32
add $r_ptr,$r_ptr,#32
bl __ecp_nistz256_sub_from @ p256_sub(res_y, S, res_y);
add sp,sp,#32*5+16 @ +16 means "skip even over saved r0-r3"
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_point_double,.-ecp_nistz256_point_double
___
}
########################################################################
# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1,
# const P256_POINT *in2);
{
my ($res_x,$res_y,$res_z,
$in1_x,$in1_y,$in1_z,
$in2_x,$in2_y,$in2_z,
$H,$Hsqr,$R,$Rsqr,$Hcub,
$U1,$U2,$S1,$S2)=map(32*$_,(0..17));
my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr);
# above map() describes stack layout with 18 temporary
# 256-bit vectors on top. Then note that we push
# starting from r0, which means that we have copy of
# input arguments just below these temporary vectors.
# We use three of them for !in1infty, !in2intfy and
# result of check for zero.
$code.=<<___;
.globl ecp_nistz256_point_add
.type ecp_nistz256_point_add,%function
.align 5
ecp_nistz256_point_add:
stmdb sp!,{r0-r12,lr} @ push from r0, unusual, but intentional
sub sp,sp,#32*18+16
ldmia $b_ptr!,{r4-r11} @ copy in2
add r3,sp,#$in2_x
orr r12,r4,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $b_ptr!,{r4-r11}
orr r12,r12,r4
orr r12,r12,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $b_ptr,{r4-r11}
cmp r12,#0
#ifdef __thumb2__
it ne
#endif
movne r12,#-1
stmia r3,{r4-r11}
str r12,[sp,#32*18+8] @ !in2infty
ldmia $a_ptr!,{r4-r11} @ copy in1
add r3,sp,#$in1_x
orr r12,r4,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $a_ptr!,{r4-r11}
orr r12,r12,r4
orr r12,r12,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $a_ptr,{r4-r11}
cmp r12,#0
#ifdef __thumb2__
it ne
#endif
movne r12,#-1
stmia r3,{r4-r11}
str r12,[sp,#32*18+4] @ !in1infty
add $a_ptr,sp,#$in2_z
add $b_ptr,sp,#$in2_z
add $r_ptr,sp,#$Z2sqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Z2sqr, in2_z);
add $a_ptr,sp,#$in1_z
add $b_ptr,sp,#$in1_z
add $r_ptr,sp,#$Z1sqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Z1sqr, in1_z);
add $a_ptr,sp,#$in2_z
add $b_ptr,sp,#$Z2sqr
add $r_ptr,sp,#$S1
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S1, Z2sqr, in2_z);
add $a_ptr,sp,#$in1_z
add $b_ptr,sp,#$Z1sqr
add $r_ptr,sp,#$S2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, Z1sqr, in1_z);
add $a_ptr,sp,#$in1_y
add $b_ptr,sp,#$S1
add $r_ptr,sp,#$S1
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S1, S1, in1_y);
add $a_ptr,sp,#$in2_y
add $b_ptr,sp,#$S2
add $r_ptr,sp,#$S2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, S2, in2_y);
add $b_ptr,sp,#$S1
add $r_ptr,sp,#$R
bl __ecp_nistz256_sub_from @ p256_sub(R, S2, S1);
orr $a0,$a0,$a1 @ see if result is zero
orr $a2,$a2,$a3
orr $a4,$a4,$a5
orr $a0,$a0,$a2
orr $a4,$a4,$a6
orr $a0,$a0,$a7
add $a_ptr,sp,#$in1_x
orr $a0,$a0,$a4
add $b_ptr,sp,#$Z2sqr
str $a0,[sp,#32*18+12]
add $r_ptr,sp,#$U1
bl __ecp_nistz256_mul_mont @ p256_mul_mont(U1, in1_x, Z2sqr);
add $a_ptr,sp,#$in2_x
add $b_ptr,sp,#$Z1sqr
add $r_ptr,sp,#$U2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, in2_x, Z1sqr);
add $b_ptr,sp,#$U1
add $r_ptr,sp,#$H
bl __ecp_nistz256_sub_from @ p256_sub(H, U2, U1);
orr $a0,$a0,$a1 @ see if result is zero
orr $a2,$a2,$a3
orr $a4,$a4,$a5
orr $a0,$a0,$a2
orr $a4,$a4,$a6
orr $a0,$a0,$a7
orrs $a0,$a0,$a4
bne .Ladd_proceed @ is_equal(U1,U2)?
ldr $t0,[sp,#32*18+4]
ldr $t1,[sp,#32*18+8]
ldr $t2,[sp,#32*18+12]
tst $t0,$t1
beq .Ladd_proceed @ (in1infty || in2infty)?
tst $t2,$t2
beq .Ladd_double @ is_equal(S1,S2)?
ldr $r_ptr,[sp,#32*18+16]
eor r4,r4,r4
eor r5,r5,r5
eor r6,r6,r6
eor r7,r7,r7
eor r8,r8,r8
eor r9,r9,r9
eor r10,r10,r10
eor r11,r11,r11
stmia $r_ptr!,{r4-r11}
stmia $r_ptr!,{r4-r11}
stmia $r_ptr!,{r4-r11}
b .Ladd_done
.align 4
.Ladd_double:
ldr $a_ptr,[sp,#32*18+20]
add sp,sp,#32*(18-5)+16 @ difference in frame sizes
b .Lpoint_double_shortcut
.align 4
.Ladd_proceed:
add $a_ptr,sp,#$R
add $b_ptr,sp,#$R
add $r_ptr,sp,#$Rsqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Rsqr, R);
add $a_ptr,sp,#$H
add $b_ptr,sp,#$in1_z
add $r_ptr,sp,#$res_z
bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_z, H, in1_z);
add $a_ptr,sp,#$H
add $b_ptr,sp,#$H
add $r_ptr,sp,#$Hsqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Hsqr, H);
add $a_ptr,sp,#$in2_z
add $b_ptr,sp,#$res_z
add $r_ptr,sp,#$res_z
bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_z, res_z, in2_z);
add $a_ptr,sp,#$H
add $b_ptr,sp,#$Hsqr
add $r_ptr,sp,#$Hcub
bl __ecp_nistz256_mul_mont @ p256_mul_mont(Hcub, Hsqr, H);
add $a_ptr,sp,#$Hsqr
add $b_ptr,sp,#$U1
add $r_ptr,sp,#$U2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, U1, Hsqr);
add $r_ptr,sp,#$Hsqr
bl __ecp_nistz256_add_self @ p256_mul_by_2(Hsqr, U2);
add $b_ptr,sp,#$Rsqr
add $r_ptr,sp,#$res_x
bl __ecp_nistz256_sub_morf @ p256_sub(res_x, Rsqr, Hsqr);
add $b_ptr,sp,#$Hcub
bl __ecp_nistz256_sub_from @ p256_sub(res_x, res_x, Hcub);
add $b_ptr,sp,#$U2
add $r_ptr,sp,#$res_y
bl __ecp_nistz256_sub_morf @ p256_sub(res_y, U2, res_x);
add $a_ptr,sp,#$Hcub
add $b_ptr,sp,#$S1
add $r_ptr,sp,#$S2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, S1, Hcub);
add $a_ptr,sp,#$R
add $b_ptr,sp,#$res_y
add $r_ptr,sp,#$res_y
bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_y, res_y, R);
add $b_ptr,sp,#$S2
bl __ecp_nistz256_sub_from @ p256_sub(res_y, res_y, S2);
ldr r11,[sp,#32*18+4] @ !in1intfy
ldr r12,[sp,#32*18+8] @ !in2intfy
add r1,sp,#$res_x
add r2,sp,#$in2_x
and r10,r11,r12
mvn r11,r11
add r3,sp,#$in1_x
and r11,r11,r12
mvn r12,r12
ldr $r_ptr,[sp,#32*18+16]
___
for($i=0;$i<96;$i+=8) { # conditional moves
$code.=<<___;
ldmia r1!,{r4-r5} @ res_x
ldmia r2!,{r6-r7} @ in2_x
ldmia r3!,{r8-r9} @ in1_x
and r4,r4,r10
and r5,r5,r10
and r6,r6,r11
and r7,r7,r11
and r8,r8,r12
and r9,r9,r12
orr r4,r4,r6
orr r5,r5,r7
orr r4,r4,r8
orr r5,r5,r9
stmia $r_ptr!,{r4-r5}
___
}
$code.=<<___;
.Ladd_done:
add sp,sp,#32*18+16+16 @ +16 means "skip even over saved r0-r3"
#if __ARM_ARCH__>=5 || defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_point_add,.-ecp_nistz256_point_add
___
}
########################################################################
# void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1,
# const P256_POINT_AFFINE *in2);
{
my ($res_x,$res_y,$res_z,
$in1_x,$in1_y,$in1_z,
$in2_x,$in2_y,
$U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..14));
my $Z1sqr = $S2;
# above map() describes stack layout with 18 temporary
# 256-bit vectors on top. Then note that we push
# starting from r0, which means that we have copy of
# input arguments just below these temporary vectors.
# We use two of them for !in1infty, !in2intfy.
my @ONE_mont=(1,0,0,-1,-1,-1,-2,0);
$code.=<<___;
.globl ecp_nistz256_point_add_affine
.type ecp_nistz256_point_add_affine,%function
.align 5
ecp_nistz256_point_add_affine:
stmdb sp!,{r0-r12,lr} @ push from r0, unusual, but intentional
sub sp,sp,#32*15
ldmia $a_ptr!,{r4-r11} @ copy in1
add r3,sp,#$in1_x
orr r12,r4,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $a_ptr!,{r4-r11}
orr r12,r12,r4
orr r12,r12,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $a_ptr,{r4-r11}
cmp r12,#0
#ifdef __thumb2__
it ne
#endif
movne r12,#-1
stmia r3,{r4-r11}
str r12,[sp,#32*15+4] @ !in1infty
ldmia $b_ptr!,{r4-r11} @ copy in2
add r3,sp,#$in2_x
orr r12,r4,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
ldmia $b_ptr!,{r4-r11}
orr r12,r12,r4
orr r12,r12,r5
orr r12,r12,r6
orr r12,r12,r7
orr r12,r12,r8
orr r12,r12,r9
orr r12,r12,r10
orr r12,r12,r11
stmia r3!,{r4-r11}
cmp r12,#0
#ifdef __thumb2__
it ne
#endif
movne r12,#-1
str r12,[sp,#32*15+8] @ !in2infty
add $a_ptr,sp,#$in1_z
add $b_ptr,sp,#$in1_z
add $r_ptr,sp,#$Z1sqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Z1sqr, in1_z);
add $a_ptr,sp,#$Z1sqr
add $b_ptr,sp,#$in2_x
add $r_ptr,sp,#$U2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, Z1sqr, in2_x);
add $b_ptr,sp,#$in1_x
add $r_ptr,sp,#$H
bl __ecp_nistz256_sub_from @ p256_sub(H, U2, in1_x);
add $a_ptr,sp,#$Z1sqr
add $b_ptr,sp,#$in1_z
add $r_ptr,sp,#$S2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, Z1sqr, in1_z);
add $a_ptr,sp,#$H
add $b_ptr,sp,#$in1_z
add $r_ptr,sp,#$res_z
bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_z, H, in1_z);
add $a_ptr,sp,#$in2_y
add $b_ptr,sp,#$S2
add $r_ptr,sp,#$S2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, S2, in2_y);
add $b_ptr,sp,#$in1_y
add $r_ptr,sp,#$R
bl __ecp_nistz256_sub_from @ p256_sub(R, S2, in1_y);
add $a_ptr,sp,#$H
add $b_ptr,sp,#$H
add $r_ptr,sp,#$Hsqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Hsqr, H);
add $a_ptr,sp,#$R
add $b_ptr,sp,#$R
add $r_ptr,sp,#$Rsqr
bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Rsqr, R);
add $a_ptr,sp,#$H
add $b_ptr,sp,#$Hsqr
add $r_ptr,sp,#$Hcub
bl __ecp_nistz256_mul_mont @ p256_mul_mont(Hcub, Hsqr, H);
add $a_ptr,sp,#$Hsqr
add $b_ptr,sp,#$in1_x
add $r_ptr,sp,#$U2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, in1_x, Hsqr);
add $r_ptr,sp,#$Hsqr
bl __ecp_nistz256_add_self @ p256_mul_by_2(Hsqr, U2);
add $b_ptr,sp,#$Rsqr
add $r_ptr,sp,#$res_x
bl __ecp_nistz256_sub_morf @ p256_sub(res_x, Rsqr, Hsqr);
add $b_ptr,sp,#$Hcub
bl __ecp_nistz256_sub_from @ p256_sub(res_x, res_x, Hcub);
add $b_ptr,sp,#$U2
add $r_ptr,sp,#$res_y
bl __ecp_nistz256_sub_morf @ p256_sub(res_y, U2, res_x);
add $a_ptr,sp,#$Hcub
add $b_ptr,sp,#$in1_y
add $r_ptr,sp,#$S2
bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, in1_y, Hcub);
add $a_ptr,sp,#$R
add $b_ptr,sp,#$res_y
add $r_ptr,sp,#$res_y
bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_y, res_y, R);
add $b_ptr,sp,#$S2
bl __ecp_nistz256_sub_from @ p256_sub(res_y, res_y, S2);
ldr r11,[sp,#32*15+4] @ !in1intfy
ldr r12,[sp,#32*15+8] @ !in2intfy
add r1,sp,#$res_x
add r2,sp,#$in2_x
and r10,r11,r12
mvn r11,r11
add r3,sp,#$in1_x
and r11,r11,r12
mvn r12,r12
ldr $r_ptr,[sp,#32*15]
___
for($i=0;$i<64;$i+=8) { # conditional moves
$code.=<<___;
ldmia r1!,{r4-r5} @ res_x
ldmia r2!,{r6-r7} @ in2_x
ldmia r3!,{r8-r9} @ in1_x
and r4,r4,r10
and r5,r5,r10
and r6,r6,r11
and r7,r7,r11
and r8,r8,r12
and r9,r9,r12
orr r4,r4,r6
orr r5,r5,r7
orr r4,r4,r8
orr r5,r5,r9
stmia $r_ptr!,{r4-r5}
___
}
for(;$i<96;$i+=8) {
my $j=($i-64)/4;
$code.=<<___;
ldmia r1!,{r4-r5} @ res_z
ldmia r3!,{r8-r9} @ in1_z
and r4,r4,r10
and r5,r5,r10
and r6,r11,#@ONE_mont[$j]
and r7,r11,#@ONE_mont[$j+1]
and r8,r8,r12
and r9,r9,r12
orr r4,r4,r6
orr r5,r5,r7
orr r4,r4,r8
orr r5,r5,r9
stmia $r_ptr!,{r4-r5}
___
}
$code.=<<___;
add sp,sp,#32*15+16 @ +16 means "skip even over saved r0-r3"
#if __ARM_ARCH__>=5 || !defined(__thumb__)
ldmia sp!,{r4-r12,pc}
#else
ldmia sp!,{r4-r12,lr}
bx lr @ interoperable with Thumb ISA:-)
#endif
.size ecp_nistz256_point_add_affine,.-ecp_nistz256_point_add_affine
___
} }}}
foreach (split("\n",$code)) {
s/\`([^\`]*)\`/eval $1/geo;
s/\bq([0-9]+)#(lo|hi)/sprintf "d%d",2*$1+($2 eq "hi")/geo;
print $_,"\n";
}
close STDOUT; # enforce flush
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